Acta mathematica scientia,Series A ›› 2001, Vol. 21 ›› Issue (zk): 665-671.
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WANG Da-Meng
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Abstract:
该文发展ＫｙＦａｎ［１］中定理４的结果，对复的Ｈｉｌｂｅｒｔ空间犎上的真压缩算子犃和单位园盘Δ 内的解析函数犳给出了优势原理．与文［５］比较，该文去掉犃为正规算子的限制，并改进了相应的结果．还对犎（Δ）的某个子类中的犳，给出‖犳′（犃）‖ 的估值．并讨论了从属关系的优势原理，特别是把ＳｈａｈＧｏｌｕｚｉｎ关于从属于单叶函数的优势半径［７，定理６．７和６．８］拓广到算子函数．
Key words: 压缩算子, 解析函数, 优势原理
CLC Number:
WANG Da-Meng. The Majorization Principle of Analytic Functions of a Proper Contraction Operators[J].Acta mathematica scientia,Series A, 2001, 21(zk): 665-671.
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１ ＦａｎＫ．Ａｎａｌｙｔｉｃｆｕｎｃｔｉｏｎｓｏｆａｐｒｏｐｅｒｃｏｎｔｒａｃｔｉｏｎ．ＭａｔｈＺ，１９７８，１６０：２７５－２９０ ２ ＦａｎＫ．Ｊｕｌｉａ＇ｓｌｅｍｍａｆｏｒｏｐｅｒａｔｏｒｓ．ＭａｔｈＡｎｎａｌｅｎ，１９７９，２３９：２４１－２４５ ３ ＡｎｄｏＴ，ＦａｎＫ．ＰｉｃｋＪｕｌｉａｔｈｅｏｒｅｍｓｆｏｒｏｐｅｒａｔｏｒｓ．ＭａｔｈＺ，１９７９，１６８：２３－３４ ４ ＦａｎＫ．Ｉｔｅｒａｔｉｏｎｏｆａｎａｌｙｔｉｃｆｕｎｃｔｉｏｎｓｏｆｏｐｅｒａｔｏｒｓ．ＭａｔｈＺ，１９８２，１７９：２９３－２９８ ５ 蹇明．算子解析函数优势原理和性质．数学物理学报，１９９２，１２（２）：２１４－２２５ ６ Ｒｕｄｉｎ Ｗ．ＦｕｎｃｔｉｏｎａｌＡｎａｌｙｓｉｓ．Ｎｅｗ Ｙｏｒｋ：ＭｃＧｒａｗＨｉｌｌ，１９７３ ７ ＤｕｒｅｎＰＬ．ＵｎｉｖａｌｅｎｔＦｕｎｃｔｉｏｎｓ．Ｎｅｗ Ｙｏｒｋ：ＳｐｒｉｎｇｅｒＶｅｒｌａｇ，１９８３ ８ 戈鲁辛著．陈建功译．复变函数的几何理论．北京：科学出版社，１９５６
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